Related papers: Differences between Lyapunov exponents for the sim…
We study some properties of the local time of the asymmetric Bernoulli walk on the line. These properties are very similar to the corresponding ones of the simple symmetric random walks in higher ($d\geq3$) dimension, which we established…
A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic…
Beyond the new results mentioned hereafter, this article aims at familiarizing researchers working in applied fields -- such as physics or economics -- with notions or formulas that they use daily without always identifying all their…
The Polya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely…
We clarify the asymptotic of the limsup of the size of the neighborhood of concentration of Sinai's walk improving the result in \cite{Pierre3}. Also we get the almost sure limit of the number of points visited more than a small but fixed…
We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d.\ matrix…
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov…
We show that the top Lyapunov exponent $\lambda_+(p)$ , $p = (p_1, \cdots, p_N)$ with $p_i >0$ for each $i$, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities $p$ whenever…
A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle…
We continue our study of intermittency for the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \xi u$, where $u\colon \Z^d\times [0,\infty)\to\R$, $\kappa$ is the diffusion constant, $\Delta$ is the discrete Laplacian,…
A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
We consider random walks in dynamic random environments given by Markovian dynamics on $\mathbb{Z}^d$. We assume that the environment has a stationary distribution $\mu$ and satisfies the Poincar\'e inequality w.r.t. $\mu$. The random walk…
We determine the rate of escape from a potential well, and the diffusion coefficient in a periodic potential, of a random walker that moves under the influence of the potential in between successive collisions with the heat bath. In the…
A general indicator of the presence of chaos in a dynamical system is the largest Lyapunov exponent. This quantity provides a measure of the mean exponential rate of divergence of nearby orbits. In this paper, we show that the so-called…
Solitons, which describe the propagation of concentrated beams of light through nonlinear media, can exhibit a variety of behaviors as a result of the intrinsic dissipation, diffraction, and the nonlinear effects. One of these phenomena,…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the…
In this paper we comment the results of ``Statistics of the Lyapunov Exponent in 1D random periodic-on-Average Systems" [Phys. Rev. Lett. {\bf 81}, 5390, 1998].